Commun. Comput. Phys., 6 (2009), pp. 483-508.

An Energy Absorbing Far-Field Boundary Condition for the Elastic Wave Equation

N. Anders Petersson 1*, Bjorn Sjogreen 1

1 Center for Applied and Scientific Computing L-550, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Received 18 July 2008; Accepted (in revised version) 22 October 2008
Available online 6 February 2009


We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. We prove stability for a second-order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.

AMS subject classifications: 65M06, 65M12, 74B05, 86A15

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Key words: Elastic wave equation, far-field boundary condition, finite differences, stability, energy estimate.

*Corresponding author.
Email: (N. A. Petersson), (B. Sjogreen)

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